CONSTRUCTION OF CLASS FIELDS OVER IMAGINARY QUADRATIC FIELDS USING y-COORDINATES OF ELLIPTIC CURVES

Abstract

By a change of variables we obtain new y-coordinates of elliptic curves. Utilizing these y-coordinates as meromorphic modular functions, together with the elliptic modular function, we generate the fields of meromorphic modular functions. Furthermore, by means of the special values of the y-coordinates, we construct the ray class fields over imaginary quadratic fields as well as normal bases of these ray class fields.